What is (\partial)/(\partial x)((5y)/(\sqrt[3]{x)}) ?

The answer to (\partial)/(\partial x)((5y)/(\sqrt[3]{x)}) is -(5y)/(3x^{4/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((5y)/(\sqrt[3]{x)})

- \frac{5 y}{3 x ^{\frac{4}{3}}}

Solution steps

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 5 y \frac{\partial}{\partial x} (x^{- \frac{1}{3}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 5 y (- \frac{1}{3} x^{- \frac{1}{3} - 1})

Simplify

5 y (- \frac{1}{3} x^{- \frac{1}{3} - 1}) : - \frac{5 y}{3 x ^{\frac{4}{3}}}

= - \frac{5 y}{3 x ^{\frac{4}{3}}}

f (x) = 2 x^{2} - 9 x + 10, at x = 1

y^{^{'}} + \frac{1}{x} y = \frac{2}{3} x^{4} y^{4}

y = x^{2} + 2 x + 11

\frac{d y}{d x} = e (3 x + 2 y)

\frac{d}{d x} (ln (3 x + 2 x^{2}))

What is (\partial)/(\partial x)((5y)/(\sqrt[3]{x)}) ?
The answer to (\partial)/(\partial x)((5y)/(\sqrt[3]{x)}) is -(5y)/(3x^{4/3)}